Places in France to visit on a limited timeline?

I’m looking at the french leg of a possible summer vacation, and it could involve starting in London, going through paris (and France, in general) on our way to Spain (either entering through San Sebastian& Basque-country OR via Barcelona)

I have about 20-25 days for this trip, with 5-6 reserved for London, and a similar amount of time for Paris.

I have several questions for you guys!

1. What is an adequate amount of time for Paris? Yes yes, I know one can spend a month exploring Paris! But what is enough time for a family not to preoccupied with seeing all the touristy sights. I was thinking 6 days would be enough, as long as we do not bite off too much that we cannot handle!

2. If we are making our way to either Barcelona or San Sebastian in Spain, it would be nice to go to 2-3 more placed in France, as we make our way to Spain! Do any of you have any suggestions?

I can tell you more about ourselves, to help. We are a family of 4, all grown up. One of which is interested in urban planning and political art, others are interested in shopping, photography, stunning scenery etc. Basically a very mixed bag!

There are countless amazing towns/cities in France to discover, but for this family sometimes, it can feel a bit repetitive going to many similar but quaint towns, so I’d like to avoid this!!

Time is tight, we would only have at most, including Paris, 11-15 days in France. Paris should take up a healthy amount of this time, as we are most interested in it and we haven’t been before.

Some places that have caught my eye:

Lyon

Dijon (so pretty)

Montpellier

So, basically, I would really like some help in coming up with a short list of really distinct and interesting places in France, preferably "on the way" to Spain, so south of Paris could be a good boundary. I’d really like to go to Mont St. Michel, but its a bit out of the way…..

Thanks so much for your help, and I would really appreciate if you could read through my question carefully, I know its a lot to ask!

Thanks again, in advance guys!
Just clarifying 20-25 days is for THE WHOLE TRIP, 11-15 days for all of France.

Mt St. Michelle is really nice.

Bordeax and Toulouse would be on your way to Spain -they are nice. The farmers market in Toulouse is pretty. Dune du Pilat is an enormous sand dune on the coast near Bordeax – that is really worth seeing if you are in the area.